Details

analyze97.0ms (2.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	24.7%	75.3%	0
0%	24.7%	75.3%	1
0%	24.7%	75.3%	2
12.4%	12.4%	75.3%	3
12.4%	12.4%	75.3%	4
18.5%	6.2%	75.3%	5
18.5%	6.2%	75.3%	6
21.6%	3.1%	75.3%	7
21.6%	3.1%	75.3%	8
23.2%	1.5%	75.3%	9
23.2%	1.5%	75.3%	10
23.9%	0.8%	75.3%	11
23.9%	0.8%	75.3%	12
24.3%	0.4%	75.3%	13
24.3%	0.4%	75.3%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.4s (37.2%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-neg_binary32`
518×	`unswap-sqr_binary32`
432×	`exp-prod_binary32`
340×	`times-frac_binary32`
333×	`associate-l_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	27	14
3	36	14
4	50	14
5	79	14
6	147	14
7	261	14
8	528	14
9	1676	14
10	3160	14
11	4121	14
12	4850	14

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize23.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
✓	0.0b	(exp.f32 (/.f32 (neg.f32 x) s))
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

series29.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
5.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite51.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

822×	`log1p-expm1-u_binary32`
822×	`expm1-log1p-u_binary32`
96×	`prod-diff_binary32`
95×	`add-sqr-sqrt_binary32`
89×	`add-log-exp_binary32`

Counts

3 → 86

Calls

3 calls:

49.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
49.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
49.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	192	27
2	2138	27
3	5221	27
0	0	0
1	0	0

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

727×	`cancel-sign-sub-inv_binary32`
632×	`fma-def_binary32`
563×	`fma-neg_binary32`
552×	`associate-/r*_binary32`
206×	`neg-mul-1_binary32`

Counts

158 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	1020
1	126	966
2	349	918
3	1445	906
4	4465	906
5	5038	906

prune49.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	3	112

Error

0.0b

Counts

112 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
	29.7b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2)))
▶	24.1b	(fma.f32 1/4 (/.f32 x s) 1/2)

Compiler

Compiled 1562 to 924 computations (40.8% saved)

localize13.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f32 1/4 (/.f32 x s) 1/2)

series5.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(fma.f32 1/4 (/.f32 x s) 1/2)

rewrite39.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

648×	`log1p-expm1-u_binary32`
648×	`expm1-log1p-u_binary32`
309×	`log-prod_binary32`
126×	`expm1-udef_binary32`
126×	`log1p-udef_binary32`

Counts

1 → 27

Calls

1 calls:

38.0ms

(fma.f32 1/4 (/.f32 x s) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	145	8
2	1661	8
3	5087	8
0	0	0
1	0	0

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary32`
3×	`*-commutative_binary32`
2×	`associate-/l*_binary32`
1×	`+-commutative_binary32`
1×	`associate-*r/_binary32`

Counts

51 → 29

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	204
1	12	168
2	17	168
3	21	168
4	23	168
5	24	168
6	24	168

prune62.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	29	3	32

Error

0.0b

Counts

32 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
▶	29.7b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2)))
✓	24.1b	(fma.f32 1/4 (/.f32 x s) 1/2)

Compiler

Compiled 389 to 255 computations (34.4% saved)

localize85.0ms (2.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f32 (/.f32 x s) 3)
✓	0.4b	(fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2))
✓	9.5b	(/.f32 (pow.f32 x 5) (pow.f32 s 5))
✓	15.5b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2)))

series91.0ms (2.5%)

Counts

4 → 72

Calls

4 calls:

39.0ms	(/.f32 (pow.f32 x 5) (pow.f32 s 5))
24.0ms	(fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2))
14.0ms	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2)))
14.0ms	(pow.f32 (/.f32 x s) 3)

rewrite67.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

303×	`log1p-udef_binary32`
176×	`prod-diff_binary32`
174×	`add-sqr-sqrt_binary32`
171×	`log1p-expm1-u_binary32`
171×	`expm1-log1p-u_binary32`

Counts

4 → 121

Calls

4 calls:

65.0ms	(pow.f32 (/.f32 x s) 3)
65.0ms	(fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2))
65.0ms	(/.f32 (pow.f32 x 5) (pow.f32 s 5))
64.0ms	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (/.f32 (pow.f32 x 5) (pow.f32 s 5)) (fma.f32 1/4 (/.f32 x s) 1/2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	372	69
2	4113	69
3	4744	69
0	0	0
1	0	0

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary32`
585×	`distribute-neg-frac_binary32`
457×	`times-frac_binary32`
379×	`associate-/l*_binary32`
334×	`fma-def_binary32`

Counts

193 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	1212
1	78	1146
2	202	1128
3	803	1011
4	3734	1011
5	5211	1011

prune108.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	136	3	139

Error

0.0b

Counts

139 → 3

Alt Table

Status	Error	Program
▶	27.9b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2)))
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
✓	24.1b	(fma.f32 1/4 (/.f32 x s) 1/2)

Compiler

Compiled 3729 to 2487 computations (33.3% saved)

localize60.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2))
✓	4.9b	(*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2)))
✓	8.1b	(/.f32 (pow.f32 x 5) (pow.f32 s 5/2))
✓	15.5b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2)))

series115.0ms (3.2%)

Counts

4 → 77

Calls

4 calls:

40.0ms	(/.f32 (pow.f32 x 5) (pow.f32 s 5/2))
37.0ms	(*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2)))
22.0ms	(fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2))
16.0ms	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2)))

rewrite76.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

210×	`add-sqr-sqrt_binary32`
204×	`log1p-expm1-u_binary32`
204×	`expm1-log1p-u_binary32`
200×	`add-cbrt-cube_binary32`
199×	`add-log-exp_binary32`

Counts

4 → 123

Calls

4 calls:

74.0ms	(fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2))
74.0ms	(*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2)))
74.0ms	(/.f32 (pow.f32 x 5) (pow.f32 s 5/2))
73.0ms	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	90
1	458	72
2	4726	72
3	4660	72
0	0	0
1	0	0

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary32`
585×	`distribute-neg-frac_binary32`
457×	`times-frac_binary32`
379×	`associate-/l*_binary32`
334×	`fma-def_binary32`

Counts

200 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1268
1	85	1208
2	214	1192
3	827	1150
4	3791	1150
5	5266	1150

prune187.0ms (5.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	140	3	143

Error

0.0b

Counts

143 → 3

Alt Table

Status	Error	Program
✓	27.9b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/480 (*.f32 (/.f32 1 (pow.f32 s 5/2)) (/.f32 (pow.f32 x 5) (pow.f32 s 5/2))) (fma.f32 1/4 (/.f32 x s) 1/2)))
✓	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
✓	24.1b	(fma.f32 1/4 (/.f32 x s) 1/2)

Compiler

Compiled 4037 to 2781 computations (31.1% saved)

regimes748.0ms (20.5%)

Accuracy

Total 0.0b remaining (37.2%)

Threshold costs 0.0b (37.2%)

Counts

85 → 1

Compiler

Compiled 15115 to 11145 computations (26.3% saved)

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
2×	`*-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	21	14
3	24	14
4	25	14
5	24	14

end90.0ms (2.5%)

Compiler: Compiled 71 to 55 computations (22.5% saved)

Details

analyze97.0ms (2.7%)

sample1.4s (37.2%)

simplify53.0ms (1.5%)

prune2.0ms (0%)

localize23.0ms (0.6%)

series29.0ms (0.8%)

rewrite51.0ms (1.4%)

simplify60.0ms (1.7%)

prune49.0ms (1.3%)

localize13.0ms (0.4%)

series5.0ms (0.1%)

rewrite39.0ms (1.1%)

simplify11.0ms (0.3%)

prune62.0ms (1.7%)

localize85.0ms (2.3%)

series91.0ms (2.5%)

rewrite67.0ms (1.8%)

simplify57.0ms (1.6%)

prune108.0ms (3%)

localize60.0ms (1.6%)

series115.0ms (3.2%)

rewrite76.0ms (2.1%)

simplify65.0ms (1.8%)

prune187.0ms (5.1%)

regimes748.0ms (20.5%)

simplify40.0ms (1.1%)

end90.0ms (2.5%)

Profiling